Question: Multiply the following complex numbers: $({4i}) \cdot ({3+5i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4i}) \cdot ({3+5i}) = $ $ ({0} \cdot {3}) + ({0} \cdot {5}i) + ({4}i \cdot {3}) + ({4}i \cdot {5}i) $ Then simplify the terms: $ (0) + (0i) + (12i) + (20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 12)i + 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 12)i - 20 $ The result is simplified: $ (0 - 20) + (12i) = -20+12i $